The need for phase unwrapping arises in several applications of coherent optics and radar. For example, phase unwrapping is one of the key requirements for terrain elevation mapping by a dual-antenna interferometric SAR (synthetic aperture radar) system. In an interferometric system, terrain elevation information is carried by the phase difference from a two-channel SAR. Initially, however, this phase is modulo-360 degrees, with discontinuities at the transition between zero and 360 degrees; that is, the phase is wrapped. The conversion to a continuous-phase function without an artificial maximum value at 360 degrees is called phase unwrapping.
Phase unwrapping is a challenging technological processing problem under realistic conditions. Various terrain conditions will ultimately cause any phase unwrapping algorithm to fail. For instance, terrains which have a low microwave reflectivity will have low signal-to-noise ratios, so that the phase will be noisy. And terrains which have large terrain gradients and/or discontinuities will cause corresponding large-phase gradients, discontinuities, and unwrapping errors in conjunction with even small amounts of noise.
The robustness of a phase unwrapping algorithm is defined by its ability to successfully unwrap these problematic kinds of data without significant errors. Two important features which characterize the robustness of a phase unwrapping algorithm are (1) its resistance to errors in the presence of noise, high gradients, and discontinuities and (2) "graceful degradation" of the output unwrapped phase in the presence of unwrapping errors. With regard to item (2), when an error occurs, ideally the algorithm recognizes that an error is likely at that point to isolate it and prevent it from propagating to other parts of the image. Isolation of errors not only limits the number of errors, but also makes it possible to remove the errors by post unwrapping filtering techniques.